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#ifndef WTFDominators_h
#define WTFDominators_h
#include <wtf/CommaPrinter.h>
#include <wtf/FastBitVector.h>
#include <wtf/GraphNodeWorklist.h>
namespace WTF {
// This is a utility for finding the dominators of a graph. Dominators are almost universally used
// for control flow graph analysis, so this code will refer to the graph's "nodes" as "blocks". In
// that regard this code is kind of specialized for the various JSC compilers, but you could use it
// for non-compiler things if you are OK with referring to your "nodes" as "blocks".
template<typename Graph>
class Dominators {
public:
using List = typename Graph::List;
Dominators(Graph& graph, bool selfCheck = false)
: m_graph(graph)
, m_data(graph.template newMap<BlockData>())
{
LengauerTarjan lengauerTarjan(m_graph);
lengauerTarjan.compute();
// From here we want to build a spanning tree with both upward and downward links and we want
// to do a search over this tree to compute pre and post numbers that can be used for dominance
// tests.
for (unsigned blockIndex = m_graph.numNodes(); blockIndex--;) {
typename Graph::Node block = m_graph.node(blockIndex);
if (!block)
continue;
typename Graph::Node idomBlock = lengauerTarjan.immediateDominator(block);
m_data[block].idomParent = idomBlock;
if (idomBlock)
m_data[idomBlock].idomKids.append(block);
}
unsigned nextPreNumber = 0;
unsigned nextPostNumber = 0;
// Plain stack-based worklist because we are guaranteed to see each block exactly once anyway.
Vector<GraphNodeWithOrder<typename Graph::Node>> worklist;
worklist.append(GraphNodeWithOrder<typename Graph::Node>(m_graph.root(), GraphVisitOrder::Pre));
while (!worklist.isEmpty()) {
GraphNodeWithOrder<typename Graph::Node> item = worklist.takeLast();
switch (item.order) {
case GraphVisitOrder::Pre:
m_data[item.node].preNumber = nextPreNumber++;
worklist.append(GraphNodeWithOrder<typename Graph::Node>(item.node, GraphVisitOrder::Post));
for (typename Graph::Node kid : m_data[item.node].idomKids)
worklist.append(GraphNodeWithOrder<typename Graph::Node>(kid, GraphVisitOrder::Pre));
break;
case GraphVisitOrder::Post:
m_data[item.node].postNumber = nextPostNumber++;
break;
}
}
if (selfCheck) {
// Check our dominator calculation:
// 1) Check that our range-based ancestry test is the same as a naive ancestry test.
// 2) Check that our notion of who dominates whom is identical to a naive (not
// Lengauer-Tarjan) dominator calculation.
ValidationContext context(m_graph, *this);
for (unsigned fromBlockIndex = m_graph.numNodes(); fromBlockIndex--;) {
typename Graph::Node fromBlock = m_graph.node(fromBlockIndex);
if (!fromBlock || m_data[fromBlock].preNumber == UINT_MAX)
continue;
for (unsigned toBlockIndex = m_graph.numNodes(); toBlockIndex--;) {
typename Graph::Node toBlock = m_graph.node(toBlockIndex);
if (!toBlock || m_data[toBlock].preNumber == UINT_MAX)
continue;
if (dominates(fromBlock, toBlock) != naiveDominates(fromBlock, toBlock))
context.reportError(fromBlock, toBlock, "Range-based domination check is broken");
if (dominates(fromBlock, toBlock) != context.naiveDominators.dominates(fromBlock, toBlock))
context.reportError(fromBlock, toBlock, "Lengauer-Tarjan domination is broken");
}
}
context.handleErrors();
}
}
bool strictlyDominates(typename Graph::Node from, typename Graph::Node to) const
{
return m_data[to].preNumber > m_data[from].preNumber
&& m_data[to].postNumber < m_data[from].postNumber;
}
bool dominates(typename Graph::Node from, typename Graph::Node to) const
{
return from == to || strictlyDominates(from, to);
}
// Returns the immediate dominator of this block. Returns null for the root block.
typename Graph::Node idom(typename Graph::Node block) const
{
return m_data[block].idomParent;
}
template<typename Functor>
void forAllStrictDominatorsOf(typename Graph::Node to, const Functor& functor) const
{
for (typename Graph::Node block = m_data[to].idomParent; block; block = m_data[block].idomParent)
functor(block);
}
// Note: This will visit the dominators starting with the 'to' node and moving up the idom tree
// until it gets to the root. Some clients of this function, like B3::moveConstants(), rely on this
// order.
template<typename Functor>
void forAllDominatorsOf(typename Graph::Node to, const Functor& functor) const
{
for (typename Graph::Node block = to; block; block = m_data[block].idomParent)
functor(block);
}
template<typename Functor>
void forAllBlocksStrictlyDominatedBy(typename Graph::Node from, const Functor& functor) const
{
Vector<typename Graph::Node, 16> worklist;
worklist.appendVector(m_data[from].idomKids);
while (!worklist.isEmpty()) {
typename Graph::Node block = worklist.takeLast();
functor(block);
worklist.appendVector(m_data[block].idomKids);
}
}
template<typename Functor>
void forAllBlocksDominatedBy(typename Graph::Node from, const Functor& functor) const
{
Vector<typename Graph::Node, 16> worklist;
worklist.append(from);
while (!worklist.isEmpty()) {
typename Graph::Node block = worklist.takeLast();
functor(block);
worklist.appendVector(m_data[block].idomKids);
}
}
typename Graph::Set strictDominatorsOf(typename Graph::Node to) const
{
typename Graph::Set result;
forAllStrictDominatorsOf(
to,
[&] (typename Graph::Node node) {
result.add(node);
});
return result;
}
typename Graph::Set dominatorsOf(typename Graph::Node to) const
{
typename Graph::Set result;
forAllDominatorsOf(
to,
[&] (typename Graph::Node node) {
result.add(node);
});
return result;
}
typename Graph::Set blocksStrictlyDominatedBy(typename Graph::Node from) const
{
typename Graph::Set result;
forAllBlocksStrictlyDominatedBy(
from,
[&] (typename Graph::Node node) {
result.add(node);
});
return result;
}
typename Graph::Set blocksDominatedBy(typename Graph::Node from) const
{
typename Graph::Set result;
forAllBlocksDominatedBy(
from,
[&] (typename Graph::Node node) {
result.add(node);
});
return result;
}
template<typename Functor>
void forAllBlocksInDominanceFrontierOf(
typename Graph::Node from, const Functor& functor) const
{
typename Graph::Set set;
forAllBlocksInDominanceFrontierOfImpl(
from,
[&] (typename Graph::Node block) {
if (set.add(block))
functor(block);
});
}
typename Graph::Set dominanceFrontierOf(typename Graph::Node from) const
{
typename Graph::Set result;
forAllBlocksInDominanceFrontierOf(
from,
[&] (typename Graph::Node node) {
result.add(node);
});
return result;
}
template<typename Functor>
void forAllBlocksInIteratedDominanceFrontierOf(const List& from, const Functor& functor)
{
forAllBlocksInPrunedIteratedDominanceFrontierOf(
from,
[&] (typename Graph::Node block) -> bool {
functor(block);
return true;
});
}
// This is a close relative of forAllBlocksInIteratedDominanceFrontierOf(), which allows the
// given functor to return false to indicate that we don't wish to consider the given block.
// Useful for computing pruned SSA form.
template<typename Functor>
void forAllBlocksInPrunedIteratedDominanceFrontierOf(
const List& from, const Functor& functor)
{
typename Graph::Set set;
forAllBlocksInIteratedDominanceFrontierOfImpl(
from,
[&] (typename Graph::Node block) -> bool {
if (!set.add(block))
return false;
return functor(block);
});
}
typename Graph::Set iteratedDominanceFrontierOf(const List& from) const
{
typename Graph::Set result;
forAllBlocksInIteratedDominanceFrontierOfImpl(
from,
[&] (typename Graph::Node node) -> bool {
return result.add(node);
});
return result;
}
void dump(PrintStream& out) const
{
for (unsigned blockIndex = 0; blockIndex < m_data.size(); ++blockIndex) {
if (m_data[blockIndex].preNumber == UINT_MAX)
continue;
out.print(" Block #", blockIndex, ": idom = ", m_graph.dump(m_data[blockIndex].idomParent), ", idomKids = [");
CommaPrinter comma;
for (unsigned i = 0; i < m_data[blockIndex].idomKids.size(); ++i)
out.print(comma, m_graph.dump(m_data[blockIndex].idomKids[i]));
out.print("], pre/post = ", m_data[blockIndex].preNumber, "/", m_data[blockIndex].postNumber, "\n");
}
}
private:
// This implements Lengauer and Tarjan's "A Fast Algorithm for Finding Dominators in a Flowgraph"
// (TOPLAS 1979). It uses the "simple" implementation of LINK and EVAL, which yields an O(n log n)
// solution. The full paper is linked below; this code attempts to closely follow the algorithm as
// it is presented in the paper; in particular sections 3 and 4 as well as appendix B.
// https://www.cs.princeton.edu/courses/archive/fall03/cs528/handouts/a%20fast%20algorithm%20for%20finding.pdf
//
// This code is very subtle. The Lengauer-Tarjan algorithm is incredibly deep to begin with. The
// goal of this code is to follow the code in the paper, however our implementation must deviate
// from the paper when it comes to recursion. The authors had used recursion to implement DFS, and
// also to implement the "simple" EVAL. We convert both of those into worklist-based solutions.
// Finally, once the algorithm gives us immediate dominators, we implement dominance tests by
// walking the dominator tree and computing pre and post numbers. We then use the range inclusion
// check trick that was first discovered by Paul F. Dietz in 1982 in "Maintaining order in a linked
// list" (see http://dl.acm.org/citation.cfm?id=802184).
class LengauerTarjan {
public:
LengauerTarjan(Graph& graph)
: m_graph(graph)
, m_data(graph.template newMap<BlockData>())
{
for (unsigned blockIndex = m_graph.numNodes(); blockIndex--;) {
typename Graph::Node block = m_graph.node(blockIndex);
if (!block)
continue;
m_data[block].label = block;
}
}
void compute()
{
computeDepthFirstPreNumbering(); // Step 1.
computeSemiDominatorsAndImplicitImmediateDominators(); // Steps 2 and 3.
computeExplicitImmediateDominators(); // Step 4.
}
typename Graph::Node immediateDominator(typename Graph::Node block)
{
return m_data[block].dom;
}
private:
void computeDepthFirstPreNumbering()
{
// Use a block worklist that also tracks the index inside the successor list. This is
// necessary for ensuring that we don't attempt to visit a successor until the previous
// successors that we had visited are fully processed. This ends up being revealed in the
// output of this method because the first time we see an edge to a block, we set the
// block's parent. So, if we have:
//
// A -> B
// A -> C
// B -> C
//
// And we're processing A, then we want to ensure that if we see A->B first (and hence set
// B's prenumber before we set C's) then we also end up setting C's parent to B by virtue
// of not noticing A->C until we're done processing B.
ExtendedGraphNodeWorklist<typename Graph::Node, unsigned, typename Graph::Set> worklist;
worklist.push(m_graph.root(), 0);
while (GraphNodeWith<typename Graph::Node, unsigned> item = worklist.pop()) {
typename Graph::Node block = item.node;
unsigned successorIndex = item.data;
// We initially push with successorIndex = 0 regardless of whether or not we have any
// successors. This is so that we can assign our prenumber. Subsequently we get pushed
// with higher successorIndex values, but only if they are in range.
ASSERT(!successorIndex || successorIndex < m_graph.successors(block).size());
if (!successorIndex) {
m_data[block].semiNumber = m_blockByPreNumber.size();
m_blockByPreNumber.append(block);
}
if (successorIndex < m_graph.successors(block).size()) {
unsigned nextSuccessorIndex = successorIndex + 1;
if (nextSuccessorIndex < m_graph.successors(block).size())
worklist.forcePush(block, nextSuccessorIndex);
typename Graph::Node successorBlock = m_graph.successors(block)[successorIndex];
if (worklist.push(successorBlock, 0))
m_data[successorBlock].parent = block;
}
}
}
void computeSemiDominatorsAndImplicitImmediateDominators()
{
for (unsigned currentPreNumber = m_blockByPreNumber.size(); currentPreNumber-- > 1;) {
typename Graph::Node block = m_blockByPreNumber[currentPreNumber];
BlockData& blockData = m_data[block];
// Step 2:
for (typename Graph::Node predecessorBlock : m_graph.predecessors(block)) {
typename Graph::Node intermediateBlock = eval(predecessorBlock);
blockData.semiNumber = std::min(
m_data[intermediateBlock].semiNumber, blockData.semiNumber);
}
unsigned bucketPreNumber = blockData.semiNumber;
ASSERT(bucketPreNumber <= currentPreNumber);
m_data[m_blockByPreNumber[bucketPreNumber]].bucket.append(block);
link(blockData.parent, block);
// Step 3:
for (typename Graph::Node semiDominee : m_data[blockData.parent].bucket) {
typename Graph::Node possibleDominator = eval(semiDominee);
BlockData& semiDomineeData = m_data[semiDominee];
ASSERT(m_blockByPreNumber[semiDomineeData.semiNumber] == blockData.parent);
BlockData& possibleDominatorData = m_data[possibleDominator];
if (possibleDominatorData.semiNumber < semiDomineeData.semiNumber)
semiDomineeData.dom = possibleDominator;
else
semiDomineeData.dom = blockData.parent;
}
m_data[blockData.parent].bucket.clear();
}
}
void computeExplicitImmediateDominators()
{
for (unsigned currentPreNumber = 1; currentPreNumber < m_blockByPreNumber.size(); ++currentPreNumber) {
typename Graph::Node block = m_blockByPreNumber[currentPreNumber];
BlockData& blockData = m_data[block];
if (blockData.dom != m_blockByPreNumber[blockData.semiNumber])
blockData.dom = m_data[blockData.dom].dom;
}
}
void link(typename Graph::Node from, typename Graph::Node to)
{
m_data[to].ancestor = from;
}
typename Graph::Node eval(typename Graph::Node block)
{
if (!m_data[block].ancestor)
return block;
compress(block);
return m_data[block].label;
}
void compress(typename Graph::Node initialBlock)
{
// This was meant to be a recursive function, but we don't like recursion because we don't
// want to blow the stack. The original function will call compress() recursively on the
// ancestor of anything that has an ancestor. So, we populate our worklist with the
// recursive ancestors of initialBlock. Then we process the list starting from the block
// that is furthest up the ancestor chain.
typename Graph::Node ancestor = m_data[initialBlock].ancestor;
ASSERT(ancestor);
if (!m_data[ancestor].ancestor)
return;
Vector<typename Graph::Node, 16> stack;
for (typename Graph::Node block = initialBlock; block; block = m_data[block].ancestor)
stack.append(block);
// We only care about blocks that have an ancestor that has an ancestor. The last two
// elements in the stack won't satisfy this property.
ASSERT(stack.size() >= 2);
ASSERT(!m_data[stack[stack.size() - 1]].ancestor);
ASSERT(!m_data[m_data[stack[stack.size() - 2]].ancestor].ancestor);
for (unsigned i = stack.size() - 2; i--;) {
typename Graph::Node block = stack[i];
typename Graph::Node& labelOfBlock = m_data[block].label;
typename Graph::Node& ancestorOfBlock = m_data[block].ancestor;
ASSERT(ancestorOfBlock);
ASSERT(m_data[ancestorOfBlock].ancestor);
typename Graph::Node labelOfAncestorOfBlock = m_data[ancestorOfBlock].label;
if (m_data[labelOfAncestorOfBlock].semiNumber < m_data[labelOfBlock].semiNumber)
labelOfBlock = labelOfAncestorOfBlock;
ancestorOfBlock = m_data[ancestorOfBlock].ancestor;
}
}
struct BlockData {
BlockData()
: parent(nullptr)
, preNumber(UINT_MAX)
, semiNumber(UINT_MAX)
, ancestor(nullptr)
, label(nullptr)
, dom(nullptr)
{
}
typename Graph::Node parent;
unsigned preNumber;
unsigned semiNumber;
typename Graph::Node ancestor;
typename Graph::Node label;
Vector<typename Graph::Node> bucket;
typename Graph::Node dom;
};
Graph& m_graph;
typename Graph::template Map<BlockData> m_data;
Vector<typename Graph::Node> m_blockByPreNumber;
};
class NaiveDominators {
public:
NaiveDominators(Graph& graph)
: m_graph(graph)
{
// This implements a naive dominator solver.
ASSERT(!graph.predecessors(graph.root()).size());
unsigned numBlocks = graph.numNodes();
// Allocate storage for the dense dominance matrix.
m_results.grow(numBlocks);
for (unsigned i = numBlocks; i--;)
m_results[i].resize(numBlocks);
m_scratch.resize(numBlocks);
// We know that the entry block is only dominated by itself.
m_results[0].clearAll();
m_results[0][0] = true;
// Find all of the valid blocks.
m_scratch.clearAll();
for (unsigned i = numBlocks; i--;) {
if (!graph.node(i))
continue;
m_scratch[i] = true;
}
// Mark all nodes as dominated by everything.
for (unsigned i = numBlocks; i-- > 1;) {
if (!graph.node(i) || !graph.predecessors(graph.node(i)).size())
m_results[i].clearAll();
else
m_results[i] = m_scratch;
}
// Iteratively eliminate nodes that are not dominator.
bool changed;
do {
changed = false;
// Prune dominators in all non entry blocks: forward scan.
for (unsigned i = 1; i < numBlocks; ++i)
changed |= pruneDominators(i);
if (!changed)
break;
// Prune dominators in all non entry blocks: backward scan.
changed = false;
for (unsigned i = numBlocks; i-- > 1;)
changed |= pruneDominators(i);
} while (changed);
}
bool dominates(unsigned from, unsigned to) const
{
return m_results[to][from];
}
bool dominates(typename Graph::Node from, typename Graph::Node to) const
{
return dominates(m_graph.index(from), m_graph.index(to));
}
void dump(PrintStream& out) const
{
for (unsigned blockIndex = 0; blockIndex < m_graph.numNodes(); ++blockIndex) {
typename Graph::Node block = m_graph.node(blockIndex);
if (!block)
continue;
out.print(" Block ", m_graph.dump(block), ":");
for (unsigned otherIndex = 0; otherIndex < m_graph.numNodes(); ++otherIndex) {
if (!dominates(m_graph.index(block), otherIndex))
continue;
out.print(" ", m_graph.dump(m_graph.node(otherIndex)));
}
out.print("\n");
}
}
private:
bool pruneDominators(unsigned idx)
{
typename Graph::Node block = m_graph.node(idx);
if (!block || !m_graph.predecessors(block).size())
return false;
// Find the intersection of dom(preds).
m_scratch = m_results[m_graph.index(m_graph.predecessors(block)[0])];
for (unsigned j = m_graph.predecessors(block).size(); j-- > 1;)
m_scratch &= m_results[m_graph.index(m_graph.predecessors(block)[j])];
// The block is also dominated by itself.
m_scratch[idx] = true;
return m_results[idx].setAndCheck(m_scratch);
}
Graph& m_graph;
Vector<FastBitVector> m_results; // For each block, the bitvector of blocks that dominate it.
FastBitVector m_scratch; // A temporary bitvector with bit for each block. We recycle this to save new/deletes.
};
struct ValidationContext {
ValidationContext(Graph& graph, Dominators& dominators)
: graph(graph)
, dominators(dominators)
, naiveDominators(graph)
{
}
void reportError(typename Graph::Node from, typename Graph::Node to, const char* message)
{
Error error;
error.from = from;
error.to = to;
error.message = message;
errors.append(error);
}
void handleErrors()
{
if (errors.isEmpty())
return;
dataLog("DFG DOMINATOR VALIDATION FAILED:\n");
dataLog("\n");
dataLog("For block domination relationships:\n");
for (unsigned i = 0; i < errors.size(); ++i) {
dataLog(
" ", graph.dump(errors[i].from), " -> ", graph.dump(errors[i].to),
" (", errors[i].message, ")\n");
}
dataLog("\n");
dataLog("Control flow graph:\n");
for (unsigned blockIndex = 0; blockIndex < graph.numNodes(); ++blockIndex) {
typename Graph::Node block = graph.node(blockIndex);
if (!block)
continue;
dataLog(" Block ", graph.dump(graph.node(blockIndex)), ": successors = [");
CommaPrinter comma;
for (auto successor : graph.successors(block))
dataLog(comma, graph.dump(successor));
dataLog("], predecessors = [");
comma = CommaPrinter();
for (auto predecessor : graph.predecessors(block))
dataLog(comma, graph.dump(predecessor));
dataLog("]\n");
}
dataLog("\n");
dataLog("Lengauer-Tarjan Dominators:\n");
dataLog(dominators);
dataLog("\n");
dataLog("Naive Dominators:\n");
naiveDominators.dump(WTF::dataFile());
dataLog("\n");
dataLog("Graph at time of failure:\n");
dataLog(graph);
dataLog("\n");
dataLog("DFG DOMINATOR VALIDATION FAILIED!\n");
CRASH();
}
Graph& graph;
Dominators& dominators;
NaiveDominators naiveDominators;
struct Error {
typename Graph::Node from;
typename Graph::Node to;
const char* message;
};
Vector<Error> errors;
};
bool naiveDominates(typename Graph::Node from, typename Graph::Node to) const
{
for (typename Graph::Node block = to; block; block = m_data[block].idomParent) {
if (block == from)
return true;
}
return false;
}
template<typename Functor>
void forAllBlocksInDominanceFrontierOfImpl(
typename Graph::Node from, const Functor& functor) const
{
// Paraphrasing from http://en.wikipedia.org/wiki/Dominator_(graph_theory):
// "The dominance frontier of a block 'from' is the set of all blocks 'to' such that
// 'from' dominates an immediate predecessor of 'to', but 'from' does not strictly
// dominate 'to'."
//
// A useful corner case to remember: a block may be in its own dominance frontier if it has
// a loop edge to itself, since it dominates itself and so it dominates its own immediate
// predecessor, and a block never strictly dominates itself.
forAllBlocksDominatedBy(
from,
[&] (typename Graph::Node block) {
for (typename Graph::Node to : m_graph.successors(block)) {
if (!strictlyDominates(from, to))
functor(to);
}
});
}
template<typename Functor>
void forAllBlocksInIteratedDominanceFrontierOfImpl(
const List& from, const Functor& functor) const
{
List worklist = from;
while (!worklist.isEmpty()) {
typename Graph::Node block = worklist.takeLast();
forAllBlocksInDominanceFrontierOfImpl(
block,
[&] (typename Graph::Node otherBlock) {
if (functor(otherBlock))
worklist.append(otherBlock);
});
}
}
struct BlockData {
BlockData()
: idomParent(nullptr)
, preNumber(UINT_MAX)
, postNumber(UINT_MAX)
{
}
Vector<typename Graph::Node> idomKids;
typename Graph::Node idomParent;
unsigned preNumber;
unsigned postNumber;
};
Graph& m_graph;
typename Graph::template Map<BlockData> m_data;
};
} // namespace WTF
using WTF::Dominators;
#endif // WTFDominators_h